Related papers: Transitive projective planes and insoluble groups

This paper is devoted to the study of noncommutative ergodic theorems for connected amenable locally compact groups. For a dynamical system $(\mathcal{M},\tau,G,\sigma)$, where $(\mathcal{M},\tau)$ is a von Neumann algebra with a normal…

Suppose that $G$ is a finite solvable group and $V$ is a finite, faithful and completely reducible $G$-module. Let $N$ be a nilpotent subgroup of $G$, then there exits $v \in V$ such that $|\bC_N(v)| \leq (|N|/p)^{1/p}$, where $p$ is the…

Let $C \subset \mathbb{P}^2$ be a plane curve of degree at least three. A point $P$ in projective plane is said to be Galois if the function field extension induced by the projection $\pi_P: C \dashrightarrow \mathbb P^1$ from $P$ is…

We study the actions of a Lie group $G$ by birationally extendible automorphisms on a domain $D\subset C^n$. For a large class of such domains defined by polynomial inequalities, all automorphisms are of this type. In the cases 1) $G$ has…

A transitive Lie algebra g of rational vector fields on a projective manifold which do not preserve any foliation determines a rational map to an algebraic homogenous space G/H which maps g to lie(G).

Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relationship and introduce a universal construction of infinite…

Let $G$ be a complex reductive group and $V$ a $G$-module. Then the $m$th jet scheme $G_m$ acts on the $m$th jet scheme $V_m$ for all $m\geq 0$. We are interested in the invariant ring $\mathcal{O}(V_m)^{G_m}$ and whether the map…

For each strongly connected finite-dimensional (pure) simplicial complex we construct a finite group, the group of projectivities of the complex, which is a combinatorial but not a topological invariant. This group is studied for…

It is shown that a transformation in the special orthogonal group SO(V) of a nondefective quadratic space over a field K is bireflectional (product of 2 involutions) if and only if it is reversible (conjugate to its inverse). Furthermore,…

A projective surface S is said to be isogenous to a product if there exist two smooth curves C, F and a finite group G acting freely on C \times F so that S=(C \times F)/G. In this paper we classify all surfaces with p_g=q=1 which are…

We propose graph theoretic equivalents for existence of a finite projective plane. We then develop a new approach and see that the problem of existence of a finite projective plane of order n is linked up with a subset of sharply 2…

While every group is isomorphic to a transitive group of permutations, the analogous property fails for inverse semigroups: not all inverse semigroups are isomorphic to transitive inverse semigroups of one-to-one partial transformations of…

Let $M$ be complex projective manifold and $A$ a positive line bundle on it. Assume that a compact and connected Lie group $G$ acts on $M$ in a Hamiltonian and holomorphic manner and that this action linearizes to $A$. Then, there is an…

Let $A$ be a Rees-like algebra of dimension $d$ and $N$ a commutative partially cancellative torsion-free seminormal monoid. We prove the following results. \begin{enumerate} \item Let $P$ be a finitely generated projective $A$-module of…

We consider groups of piecewise-projective homeomorphisms of the line which are known to be non-amenable using notably the Carriere--Ghys theorem on ergodic equivalence relations. Replacing that theorem by an explicit fixed-point argument,…

We say that a group G acts infinitely transitively on a set X if for every integer m the induced diagonal action of G is transitive on the cartesian mth power of X with the diagonals removed. We describe three classes of affine algebraic…

For every p >= 5, we determine all Z_p-invariant nonsingular quartic surfaces in the three dimensional projective space over an algebraically closed field of characteristic zero. In some cases, we also determine their full projective…

It is known that if the special automorphism group $\text{SAut}(X)$ of a quasiaffine variety $X$ of dimension at least $2$ acts transitively on $X$, then this action is infinitely transitive. In this paper we address the question whether…

A G-solenoid is a laminated space whose leaves are copies of a single Lie group G, and whose transversals are totally disconnected sets. It inherits a G-action and can be considered as dynamical system. Free Z^d-actions on the Cantor set as…

We prove that if $G$ and $H$ are finite metacyclic groups with isomorphic rational group algebras and one of them is nilpotent then $G$ and $H$ are isomorphic.